Download R Commands for Numeric Summaries of Data and Boxplots 1. Mean

R Commands for Numeric Summaries of Data and Boxplots
1. Mean, Median, Standard deviation, and Quartiles: The command sequence is Statistics | Summaries |
Numerical Summaries… A dialog box will pop up. Select the variable or variables you want to
summarize from the drop down menu. You may also obtain separate summaries for groups in this
dialog box by clicking on the “Summarize by groups” button. Note that median = 50th percentile = 50%
in this output.
a. Exercise: Import the 4th-6th graders Popularity Study data from the course website. Use R
Commander to computer the mean, median, standard deviation, etc. of the Sports variable for
girls and boys. This variable represents how the student ranked sports as to its importance for
popularity by assigning a ranking of 1, 2, 3 or 4 where 1= most important for popularity,
4=least important for popularity.
Mean Median Standard Deviation Sample Size
Boys
Girls
b. Comment on your results from part (a). What similarities or differences do you observe for
Sports ranking between boys and girls? Is this finding unexpected?
2. Z-scores or standardized scores: To obtain a z-score for every value in your data set, select Data |
Manage variables in active data set | Standardize variables. Every data value in your data set will
be converted to a z-score = (data value – mean of data set)/ (standard deviation of data set). The zscores are stored in a new column in your data set. You can view the z-scores by clicking the “View
data set” button at the top of the R Commander window.
a. Import the “Income per capita by country” data set from the course website. Calculate the zscore for income per capita. Do any countries have |z| >3? List them ___________________
What does it mean for a country to have a z-score whose absolute value is over 3?
b. Is “income per capita” skewed or symmetric?
c. Calculate the mean and standard deviation of income per capita. Calculate the interval
3
,
3
=_______________________ According to Chebychev’s Rule, at least what percent
of the incomes will fall in this interval? _________ What percent falls in the interval according
to the Empirical Rule?________. Verify that the Empirical Rule does NOT give the correct
answer for these data. Why? ________________________ Does Chebychev’s work?_____
3. Boxplots: Select Graphs | Boxplot. Select the variable you want to plot in the drop down menu of the
resulting dialog box. If you want separate boxplots of the variable for two groups (for example, scores
by gender), click the “Plot by groups” button and select the categorical variable you’d like to group on.